Derivatives of Inverse Trigonometric Functions

Flashcards covering derivative formulas and notation conventions for inverse trigonometric functions.

Derivative of $y = \tan^{-1}(u)$

$$\frac{dy}{dx} = \frac{u'}{1 + u^2}$$

Derivative of $y = \cot^{-1}(u)$

$$\frac{dy}{dx} = -\frac{u'}{1 + u^2}$$

Derivative of $y = \sec^{-1}(u)$

$$\frac{dy}{dx} = \frac{u'}{|u|\sqrt{u^2 - 1}}$$

Derivative of $y = \csc^{-1}(u)$

$$\frac{dy}{dx} = -\frac{u'}{|u|\sqrt{u^2 - 1}}$$

Derivative of $y = \sin^{-1}(u)$

$$\frac{dy}{dx} = \frac{u'}{\sqrt{1 - u^2}}$$

Derivative of $y = \cos^{-1}(u)$

$$\frac{dy}{dx} = -\frac{u'}{\sqrt{1 - u^2}}$$

$$u(x)$$

The "inside function" used within the inverse trigonometric derivative formulas.

Inverse Trigonometric Function Notation

Notation that may be indicated using the inverse function notation $f^{-1}$ or with the prefix 'arc' (e.g., $\sin^{-1}(x) = \arcsin(x)$).